If (\pi) and(\pi), then. | MATH - CONJUGATE, MODULUS AND ARGUMENT OF COMPLEX NUMBERS | SolveeIt

If $\pi$ and $\pi$ , then.

$z$

${Im}(z) > 0$

$arg(z)$

$\pi$

Answer

${Im}(z) > 0$

Explanation

Let ${\bar{z}}_{2} = 3 - 5i$

Then $\frac{{\bar{z}}_{2}z_{1}}{z_{2}} = \frac{(3 - 5i)(1 + 2i)}{(3 + 5i)} = \frac{13 + i}{3 + 5i}$

And $\frac{13 + i}{3 + 5i} \times \frac{3 - 5i}{3 - 5i} = \frac{44 - 62i}{34}$

⇒ ${Re}\left( \frac{{\bar{z}}_{2}z_{1}}{z_{2}} \right) = \frac{44}{34} = \frac{22}{17}$

$(3 + i)z = (3 - i)\bar{z}z = x(3 - i)x \in R$ .

Question: If \(\pi\) and\(\pi\), then....